Such a tool holder is known from DE 100 65 383 A1. There, several slits or recesses which reduce the radial heat conduction cross-section are provided in a circumference part of a front clamping area, which lies radially on the inside. By means of such slits, the expansion of the front clamping area achieved by heating is improved and less material must be heated in the clamping area of the receiving body, in order to achieve the widening needed for the insertion of the tools. Since the material essential for the widening lies on the outside, a lower introduction of heat or a more rapid widening is also possible with the heat acting from the outside. In this way, the tool holders can also have smaller dimensions. However, the production of such slits is relatively expensive, particularly for small tool holders, since the slits cannot be formed continuously as a result of the usually present threaded connections for cooling agent transfer tubes or other connecting parts of an interior cooling agent supply.